Question

For the elementary reaction \( P \to Q \), the rate of disappearance of ‘P’ increases by a factor of 8 upon doubling the concentration of ‘P’. The order of the reaction with respect to ‘P’ is:

• A. 3
• B. 4
• C. 2
• D. 1

Hint:

The reaction order is determined by analyzing how the rate changes with concentration variation.

Answer 1

The Correct Option is A

The rate law for a reaction is given by: \[ \text{Rate} = k [P]^n \] where \( n \) is the order of reaction. Given that doubling the concentration of \( P \) causes the rate to increase by a factor of 8, we can write: \[ \frac{\text{Rate}_2}{\text{Rate}_1} = \left( \frac{[P]_2}{[P]_1} \right)^n \] Substituting the values: \[ 8 = \left( \frac{2[P]}{[P]} \right)^n \] \[ 8 = 2^n \] Since \( 2^3 = 8 \), we get: \[ n = 3 \] Thus, the order of the reaction with respect to \( P \) is 3.